Noise-Aware Differentially Private Variational Inference (2410.19371v2)

Abstract: Differential privacy (DP) provides robust privacy guarantees for statistical inference, but this can lead to unreliable results and biases in downstream applications. While several noise-aware approaches have been proposed which integrate DP perturbation into the inference, they are limited to specific types of simple probabilistic models. In this work, we propose a novel method for noise-aware approximate Bayesian inference based on stochastic gradient variational inference which can also be applied to high-dimensional and non-conjugate models. We also propose a more accurate evaluation method for noise-aware posteriors. Empirically, our inference method has similar performance to existing methods in the domain where they are applicable. Outside this domain, we obtain accurate coverages on high-dimensional Bayesian linear regression and well-calibrated predictive probabilities on Bayesian logistic regression with the UCI Adult dataset.

• The paper introduces NA-DPVI, a novel method that integrates DP noise into Bayesian inference to improve uncertainty quantification.
• It establishes a formal framework using Bayesian linear models to post-process gradient traces and analyze hyperparameter effects.
• Empirical evaluations in high-dimensional Bayesian linear and logistic regression show improved calibration on real-world datasets.

Noise-Aware Differentially Private Variational Inference

The paper presents a novel approach to incorporating differential privacy (DP) into Bayesian inference by proposing Noise-Aware Differentially Private Variational Inference (NA-DPVI). Traditional methods suffer from poor uncertainty quantification due to disregarding the noise added for privacy purposes. The proposed NA-DPVI method effectively integrates DP noise into high-dimensional and non-conjugate probabilistic models, offering a significant enhancement over existing techniques limited to simpler models.

Key Contributions

The authors make several important contributions:

1. Theoretical Framework: A formal framework for noise-aware inference is established, expanding upon previous work to allow for more comprehensive analysis of approximate noise-aware posteriors.
2. NA-DPVI Method: A new methodology is introduced for performing approximate noise-aware inference by post-processing gradient traces using a Bayesian linear model. This captures uncertainty from DP while utilizing VI posterior approximations for data modeling.
3. Theoretical Analysis: The paper provides a rigorous examination of conditions under which the proposed method is effective, focusing on the influence of hyperparameters, such as learning rates, on posterior approximation.
4. Evaluation Method: An advanced evaluation technique is developed for estimating noise-aware posteriors, adapted from the TARP method. This is used to gauge the effectiveness of the NA-DPVI method in empirical tests.

Numerical Results and Experiments

The empirical evaluation demonstrates that NA-DPVI performs comparably to traditional methods when they are applicable, with enhanced accuracy in scenarios where they are not. Specifically, the paper reports strong results in high-dimensional Bayesian linear regression and Bayesian logistic regression with the UCI Adult dataset.

• Exponential Families: NA-DPVI achieves competitive coverage errors compared to existing noise-aware techniques, proving its efficacy across various conjugate models.
• High-Dimensional Models: In scenarios such as 10D Bayesian linear regression, NA-DPVI shows substantially improved results over naive baselines, particularly when using more robust inference techniques like NUTS.
• Real-World Data: The model's real-world applicability is illustrated through Bayesian logistic regression on the UCI Adult dataset, where NA-DPVI achieves better calibrated predictive distributions.

Implications and Future Directions

This paper's contributions are two-fold, impacting both theoretical understanding and practical execution of DP Bayesian inference. By incorporating noise-awareness into the inference process, NA-DPVI enables more precise uncertainty quantification in private data analysis. Future research could focus on further refining these techniques and extending their applicability to broader classes of models and datasets.

Moreover, the framework and methodology pave the way for future exploration in noise-aware inference algorithms that could offer even more robust solutions for incorporating DP in various fields. Continued investigation into the implications of privacy noise on statistical inference accuracy remains a critical area of development.

In conclusion, the framework and results presented constitute a substantial step forward in noise-aware Bayesian inference under differential privacy, promising more reliable applications in data-sensitive environments.